(logX)(2logX+1)=6

Solution for (logX)(2logX+1)=6 equation:

Simplifying
(logX)(2logX + 1) = 6

Reorder the terms:
gloX(1 + 2gloX) = 6
(1 * gloX + 2gloX * gloX) = 6
(1gloX + 2g2l2o2X2) = 6

Solving
1gloX + 2g2l2o2X2 = 6

Solving for variable 'g'.

Reorder the terms:
-6 + 1gloX + 2g2l2o2X2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + 1gloX + 2g2l2o2X2 = 0

Factor a trinomial.
(-2 + -1gloX)(3 + -2gloX) = 0

Subproblem 1
Set the factor '(-2 + -1gloX)' equal to zero and attempt to solve:

Simplifying
-2 + -1gloX = 0

Solving
-2 + -1gloX = 0

Move all terms containing g to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + -1gloX = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1gloX = 0 + 2
-1gloX = 0 + 2

Combine like terms: 0 + 2 = 2
-1gloX = 2

Divide each side by '-1loX'.
g = -2l-1o-1X-1

Simplifying
g = -2l-1o-1X-1
Subproblem 2
Set the factor '(3 + -2gloX)' equal to zero and attempt to solve:

Simplifying
3 + -2gloX = 0

Solving
3 + -2gloX = 0

Move all terms containing g to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -2gloX = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2gloX = 0 + -3
-2gloX = 0 + -3

Combine like terms: 0 + -3 = -3
-2gloX = -3

Divide each side by '-2loX'.
g = 1.5l-1o-1X-1

Simplifying
g = 1.5l-1o-1X-1
Solution
g = {-2l-1o-1X-1, 1.5l-1o-1X-1}